280 Wisconsin Academy of Sciences , Arts and Letters. 
In determining the difference in distribution, the angles observed were 
quite small. The largest was less than 2 s , making the angular throw of 
the needle less than 1°. The deflections in scale divisions were there- 
3- 
fore taken as proportional to sin The error in the case of the largest 
reading would not exceed one part in 3,500. The error in the result is 
still less, as it is obtained by subtracting two throws. 
Specimen Calculation. 
Magnet A. 
Middle to North End. 
Steps. 
Average 
observed 
throw at 
11° C. 
Average 
observed 
throw at 
99.°5 C. 
Corrected 
throw at 
99.°5 C. 
Difference 
in distribu¬ 
tion in 
scale 
divisions. 
Difference 
in distribu¬ 
tion in 
C. G. S. 
lines of 
inductions. 
I. 
18.0 
17.5 
18.3 
— 0.3 
— 0.4 
II. .. 
18.4 
18.1 
18.9 
— 0.5 
— 0.7 
Ill. 
11.8 
12.6 
13.2 
— 1.4 
— 2.0 
IV. 
— 7.2 
— 4.2 
— 4.4 
— 2.8 
— 3.9 
V.... 
—34.3 
—27.2 
—28.4 
— 5.9 
— 8.3 
VI. 
—42.0 
—27.7 
—28.9 
—13.1 
—18.3 
VII. 
—49.0 
—19.4 
—20.3 
—28.7 
—40.2 
End. 
— 5.4 
— 2.2 
— 2.3 
— 3.1 
- 4.3 
In finding the sum of the distributions it was found necessary to make 
use of the formula given on p. 279, because the angles were too large to 
3 
take sin proportional to tan 2 3. The corrected readings were re- 
A 
duced to absolute measure in the way just described. We have now the 
sum and difference of the linear distribution of the two magnets. One- 
half the sum plus one-half the difference gives the distribution of one, 
one-half the sum minus one-half the difference gives that of the other. 
The distributions at the higher temperature were obtained by subtract¬ 
ing the change in distribution due to the heating. 
The induction at each point of the magnet was obtained by adding 
up the number of lines of induction passing out of the magnet beyond 
the point in question. 
